Determining a value of a variable on an rf transmission model

ABSTRACT

Systems and methods for determining a value of a variable on a radio frequency (RF) transmission model are described. One of the methods includes identifying a complex voltage and current measured at an output of an RF generator and generating an impedance matching model based on electrical components defined in an impedance matching circuit coupled to the RF generator. The method further includes propagating the complex voltage and current through the one or more elements from the input of the impedance matching model and through one or more elements of an RF transmission model portion that is coupled to the impedance matching model to determine a complex voltage and current at the output of the RF transmission model portion.

CLAIM OF PRIORITY

This application is a continuation of and claims priority, under 35U.S.C. 120, to U.S. application Ser. No. 13/717,538, filed Dec. 17,2012, titled “Determining a Value of a Variable on an RF TransmissionModel”, which is incorporated by reference herein in its entirety.

FIELD

The present embodiments relate to determining a value of a variable on aradio frequency (RF) transmission line.

BACKGROUND

In a plasma-based system, plasma is generated when a process gas issupplied within a plasma chamber and radio frequency (RF) power issupplied to an electrode within the plasma chamber. The plasma-basedsystem is used to perform various operations on a wafer. For example,the plasma is used to etch the wafer, deposit materials on the wafer,clean the wafer, etc.

During the performance of the operations, a point within theplasma-based system may be monitored to determine whether theplasma-based system is operating properly. The point is monitored usinga probe. However, it may be expensive to use the probe within theplasma-based system. For example, some entities may avoid using theprobe to avoid the cost of the probe. Such avoidance of use of the probemay result in not knowing whether the plasma-based system is operatingproperly.

It is in this context that embodiments described in the presentdisclosure arise.

SUMMARY

Embodiments of the disclosure provide apparatus, methods and computerprograms for determining a value of a variable on a radio frequency (RF)transmission line. It should be appreciated that the present embodimentscan be implemented in numerous ways, e.g., a process, an apparatus, asystem, a piece of hardware, or a method on a computer-readable medium.Several embodiments are described below.

In various embodiments, a computer-generated model of an RF transmissionline is used to determine a variable, e.g., a complex voltage, a complexcurrent, a complex voltage and current, complex power, etc., at anoutput of the model. Instead of a metrology tool, e.g., a probe, thevariable is used within a plasma system to determine whether the plasmasystem is functioning properly.

In some embodiments, a method for determining a value of a variable on aradio frequency (RF) transmission model is described. The methodincludes identifying a first complex voltage and current measured at anoutput of an RF generator when the RF generator is coupled to a plasmachamber via an impedance matching circuit. The impedance matchingcircuit has an input coupled to the output of the RF generator and anoutput coupled to an RF transmission line. The method includesgenerating an impedance matching model based on electrical componentsdefined in the impedance matching circuit. The impedance matching modelhas an input and an output. The input of the impedance matching model isused for receiving the first complex voltage and current. Also, theimpedance matching model has one or more elements. The method furtherincludes propagating the first complex voltage and current through theone or more elements from the input of the impedance matching model tothe output of the impedance matching model to determine a second complexvoltage and current. The second complex voltage and current is at theoutput of the impedance matching model. The method includes generatingan RF transmission model based on circuit components defined in the RFtransmission line. The RF transmission model has an input and an output.The input of the RF transmission model is coupled to the output of theimpedance matching model. The RF transmission model has a portion thatincludes one or more elements. The method includes propagating thesecond complex voltage and current through the one or more elements ofthe RF transmission model portion from the input of the RF transmissionmodel to an output of the RF transmission model portion to determine athird complex voltage and current. The third complex voltage and currentis a complex voltage and current at the output of the RF transmissionmodel portion.

In various embodiments, a plasma system for determining a value of avariable on an RF transmission model is described. The plasma systemincludes an RF generator for generating an RF signal. The RF generatoris associated with a voltage and current probe. The voltage and currentprobe is configured to measure a first complex voltage and current at anoutput of the RF generator. The plasma system further includes animpedance matching circuit coupled to the RF generator and a plasmachamber coupled to the impedance matching circuit via an RF transmissionline. The impedance matching circuit has an input coupled to the outputof the RF generator and an output coupled to the RF transmission line.The plasma system includes a processor coupled to the RF generator. Theprocessor is used for identifying the first complex voltage and currentand generating an impedance matching model based on electricalcomponents defined in the impedance matching circuit. The impedancematching model has an input and an output. The input of the impedancematching model receives the first complex voltage and current. Moreover,the impedance matching model has one or more elements. The methodincludes propagating the first complex voltage and current through theone or more elements from the input of the impedance matching model tothe output of the impedance matching model to determine a second complexvoltage and current. The second complex voltage and current is a complexvoltage and current at the output of the impedance matching model. Themethod includes generating an RF transmission model based on electricalcomponents defined in the RF transmission line. The RF transmissionmodel has an input and an output. The input of the RF transmission modelis coupled to the output of the impedance matching model. Also, the RFtransmission model portion has a portion that includes one or moreelements. The method includes propagating the second complex voltage andcurrent through the one or more elements of the RF transmission modelportion from the input of the RF transmission model to an output of theRF transmission model portion to determine a third complex voltage andcurrent. The third complex voltage and current is a complex voltage andcurrent at the output of the RF transmission model portion. The methodincludes providing the third complex voltage and current for storage toa storage hardware unit.

In some embodiments, a computer system for determining a value of avariable on an RF transmission model is described. The computer systemincludes a processor. The processor is configured to identify a firstcomplex voltage and current measured at an output of an RF generatorwhen the RF generator is coupled to a plasma chamber via an impedancematching circuit. The impedance matching circuit has an input coupled tothe output of the RF generator and an output coupled to an RFtransmission line. The processor is further configured to generate animpedance matching model based on electrical components defined in theimpedance matching circuit. The impedance matching model has an inputand an output. The input of the impedance matching model receives thefirst complex voltage and current. Also, the impedance matching modelhas one or more elements. The processor is configured to propagate thefirst complex voltage and current through the one or more elements fromthe input of the impedance matching model to the output of the impedancematching model to determine a second complex voltage and current at theoutput of the impedance matching model. The processor is also configuredto generate an RF transmission model based on electrical componentsdefined in the RF transmission line. The RF transmission model has aninput and an output. The input of the RF transmission model is coupledto the output of the impedance matching model. The RF transmission modelhas a portion that includes one or more elements. The processor isconfigured to propagate the second complex voltage and current throughthe one or more elements of the RF transmission model portion from theinput of the RF transmission model to an output of the RF transmissionmodel portion to determine a third complex voltage and current at theoutput of the RF transmission model portion. The computer systemincludes a memory device coupled to the processor. The memory device isconfigured to store the third complex voltage and current.

Some advantages of the above-described embodiments include reducing achance of using a metrology tool at a node of a plasma system duringproduction, which includes performance of processes on a work piece.Examples of the processes include cleaning, depositing, etching, etc. Avoltage and current probe that is calibrated according to a pre-setformula is used to accurately sense values and the accurately sensedvalues are propagated as described above to generate accurate values ofthe variable at one or more nodes of a model of plasma system. Thepre-set formula may be a standard. For example, the voltage and currentprobe is calibrated according to National Institute of Standards andTechnology (NIST) standard, which is rigid. Hence, usage of the voltageand current probe results in values of the variable that are accurate.During production, the generated values are used to determine whetherone or more parts, e.g., an impedance matching circuit, an RF generator,a cable, an RF transmission line, a portion of the RF transmission line,etc., of a plasma system that excludes the metrology tool are workingappropriately. Instead of using the metrology tool at a node duringproduction, the generated accurate values at the node are used duringthe production to determine whether one or more parts are workingappropriately, e.g., functioning, operational, etc.

Other advantages of the above-described embodiments include reducingchances of unconfinement of plasma from a plasma chamber and arcingwithin the plasma chamber. Plasma within plasma chamber is confined toperform various processes on a work piece within the plasma chamber.With an increase in unconfinement of the plasma, effectiveness of theplasma on the work piece is reduced. Also, arcing within the plasmachamber is to be detected. In some embodiments, arcing is a suddenrelease of energy between parts in the plasma chamber. By consideringboth voltage and current in determining a variable, e.g., impedance,model bias voltage, etc., at the plasma chamber, the unconfinement andthe arcing may be more accurately detected at the plasma chamber thanusing the voltage alone. For example, the variable is determined at theplasma chamber by using the voltage and current probe. The variable isthen used during production to accurately determine whether there isunconfinement and/or arcing.

Other aspects will become apparent from the following detaileddescription, taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments may best be understood by reference to the followingdescription taken in conjunction with the accompanying drawings.

FIG. 1 is a block diagram of a system for determining the variable at anoutput of an impedance matching model and at an output of a portion of aradio frequency (RF) transmission model, in accordance with anembodiment described in the present disclosure.

FIG. 2 is a flowchart of a method for determining a complex voltage andcurrent at the output of the RF transmission model portion, inaccordance with an embodiment described in the present disclosure.

FIG. 3A is a block diagram of a system used to illustrate an impedancematching circuit, in accordance with an embodiment described in thepresent disclosure.

FIG. 3B is a circuit diagram of an impedance matching model, inaccordance with an embodiment described in the present disclosure.

FIG. 4 is a diagram of a system used to illustrate an RF transmissionline, in accordance with an embodiment described in the presentdisclosure.

FIG. 5A is a block diagram of a system used to illustrate a circuitmodel of the RF transmission line, in accordance with an embodimentdescribed in the present disclosure.

FIG. 5B is a diagram of an electrical circuit used to illustrate atunnel and strap model of the RF transmission model, in accordance withan embodiment described in the present disclosure.

FIG. 6 is a block diagram of a plasma system that includes filters usedto determine the variable, in accordance with an embodiment described inthe present disclosure.

FIG. 7A is a diagram of a system used to illustrate a model of thefilters to improve an accuracy of the variable, in accordance with anembodiment described in the present disclosure.

FIG. 7B is a diagram of a system used to illustrate a model of thefilters, in accordance with an embodiment described in the presentdisclosure.

FIG. 8 is a block diagram of a system for using a current and voltage(VI) probe to measure the variable at an output of an RF generator ofthe system of FIG. 1, in accordance with one embodiment described in thepresent disclosure.

FIG. 9 is a block diagram of a system in which the VI probe and acommunication device are located outside the RF generator, in accordancewith an embodiment described in the present disclosure.

FIG. 10 is a block diagram of an embodiment of a system in which valuesof the variable determined using the system of FIG. 1 are used, inaccordance with an embodiment described in the present disclosure.

FIG. 11A is a diagram of a graph that illustrates a correlation betweenvoltage that is measured at an output within the system of FIG. 1 byusing a voltage probe and a voltage that is determined using the methodof FIG. 2 when an x MHz RF generator is operational, in accordance withan embodiment described in the present disclosure.

FIG. 11B is a diagram of a graph that illustrates a correlation betweenvoltage that is measured at an output within the system of FIG. 1 byusing a voltage probe and a voltage that is determined using the methodof FIG. 2 when a y MHz RF generator is operational, in accordance withan embodiment described in the present disclosure.

FIG. 11C is a diagram of a graph that illustrates a correlation betweenvoltage that is measured at an output within the system of FIG. 1 byusing a voltage probe and a voltage that is determined using the methodof FIG. 2 when a z MHz RF generator is operational, in accordance withone embodiment described in the present disclosure.

FIG. 12A is a diagram of graphs used to illustrate a correlation betweena wired wafer bias measured using a sensor tool, a model bias that isdetermined using the method of FIG. 2 and using a mathematicalconversion, and an error in the model bias when the x MHz RF generatoris operational, in accordance with an embodiment described in thepresent disclosure.

FIG. 12B is a diagram of graphs used to illustrate a correlation betweena wired wafer bias measured using a sensor tool, a model bias that isdetermined using the method of FIG. 2 and using a mathematicalconversion, and an error in the model bias when the y MHz RF generatoris operational, in accordance with one embodiment described in thepresent disclosure.

FIG. 12C is a diagram of graphs used to illustrate a correlation betweena wired wafer bias measured using a sensor tool, a model bias that isdetermined using the method of FIG. 2 and using a mathematicalconversion, and an error in the model bias when the z MHz RF generatoris operational, in accordance with one embodiment described in thepresent disclosure.

FIG. 12D is a diagram of graphs used to illustrate a correlation betweena wired wafer bias measured using a sensor tool, a model bias that isdetermined using the method of FIG. 2 and using a mathematicalconversion, and an error in the model bias when the x and y MHz RFgenerators are operational, in accordance with an embodiment describedin the present disclosure.

FIG. 12E is a diagram of graphs used to illustrate a correlation betweena wired wafer bias measured using a sensor tool, a model bias that isdetermined using the method of FIG. 2 and using a mathematicalconversion, and an error in the model bias when the x and z MHz RFgenerators are operational, in accordance with an embodiment describedin the present disclosure.

FIG. 12F is a diagram of graphs used to illustrate a correlation betweena wired wafer bias measured using a sensor tool, a model bias that isdetermined using the method of FIG. 2 and using a mathematicalconversion, and an error in the model bias when the y and z MHz RFgenerators are operational, in accordance with an embodiment describedin the present disclosure.

FIG. 12G is a diagram of graphs used to illustrate a correlation betweena wired wafer bias measured using a sensor tool, a model bias that isdetermined using the method of FIG. 2 and using a mathematicalconversion, and an error in the model bias when the x, y, and z MHz RFgenerators are operational, in accordance with an embodiment describedin the present disclosure.

FIG. 13 is a block diagram of a host system of the system of FIG. 2, inaccordance with an embodiment described in the present disclosure.

DETAILED DESCRIPTION

The following embodiments describe systems and methods for determining avalue of a variable on a radio frequency (RF) transmission line. It willbe apparent that the present embodiments may be practiced without someor all of these specific details. In other instances, well known processoperations have not been described in detail in order not tounnecessarily obscure the present embodiments.

FIG. 1 is a block diagram of an embodiment of a system 126 fordetermining the variable at an output of an impedance matching model 104and at an output, e.g., a model node N1 m, of a portion 173 of an RFtransmission model 161, which is a model of an RF transmission line 113.The RF transmission line 113 has an output, e.g., a node N2. A voltageand current (VI) probe 110 measures a complex voltage and current Vx,Ix, and □x, e.g., a first complex voltage and current, at an output,e.g., a node N3, of an x MHz RF generator. It should be noted that Vxrepresents a voltage magnitude, Ix represents a current magnitude, and□x represents a phase between Vx and Ix. The impedance matching model104 has an output, e.g., a model node N4 m.

Moreover, a VI probe 111 measures a complex voltage and current Vy, Iy,and □y at an output, e.g., a node N5, of a y MHz RF generator. It shouldbe noted that Vy represents a voltage magnitude, Iy represents a currentmagnitude, and □y represents a phase between Vy and Iy.

In some embodiments, a node is an input of a device, an output of adevice, or a point within the device. A device, as used herein, isdescribed below.

Examples of x MHz include 2 MHz, 27 MHz, and 60 MHz. Examples of y MHzinclude 2 MHz, 27 MHz, and 60 MHz. The x MHz is different than y MHz.For example, when x MHz is 2 MHz, y MHz is 27 MHz or 60 MHz. When x MHzis 27 MHz, y MHz is 60 MHz.

An example of each VI probe 110 and 111 includes a VI probe thatcomplies with a pre-set formula. An example of the pre-set formulaincludes a standard that is followed by an Association, which developsstandards for sensors. Another example of the pre-set formula includes aNational Institute of Standards and Technology (NIST) standard. As anillustration, the VI probe 110 or 111 is calibrated according to NISTstandard. In this illustration, the VI probe 110 or 111 is coupled withan open circuit, a short circuit, or a known load to calibrate the VIprobe 110 or 111 to comply with the NIST standard. The VI probe 110 or111 may first be coupled with the open circuit, then with the shortcircuit, and then with the known load to calibrate the VI probe 110based on NIST standard. The VI probe 110 or 111 may be coupled to theknown load, the open circuit, and the short circuit in any order tocalibrate the VI probe 110 or 111 according to NIST standard. Examplesof a known load include a 50 ohm load, a 100 ohm load, a 200 ohm load, astatic load, a direct current (DC) load, a resistor, etc. As anillustration, each VI probe 110 and 111 is calibrated accordingNIST-traceable standards.

The VI probe 110 is coupled to the output, e.g., the node N3, of the xMHz RF generator. The output, e.g., the node N3, of the x MHz RFgenerator is coupled to an input 153 of an impedance matching circuit114 via a cable 150. Moreover, the VI probe 111 is coupled to theoutput, e.g., the node N5, of the y MHz RF generator. The output, e.g.,the node N5, of the y MHz RF generator is coupled to another input 155of an impedance matching circuit 114 via a cable 152.

An output, e.g., a node N4, of the impedance matching circuit 114 iscoupled to an input of the RF transmission line 113. The RF transmissionline 113 includes a portion 169 and another portion 195. An input of theportion 169 is an input of the RF transmission line 113. An output,e.g., a node N1, of the portion 169 is coupled to an input of theportion 195. An output, e.g., the node N2, of the portion 195 is coupledto the plasma chamber 175. The output of the portion 195 is the outputof the RF transmission line 113. An example of the portion 169 includesan RF cylinder and an RF strap. The RF cylinder is coupled to the RFstrap. An example of the portion 195 includes an RF rod and/or a supportfor supporting the plasma chamber 175.

The plasma chamber 175 includes an electrostatic chuck (ESC) 177, anupper electrode 179, and other parts (not shown), e.g., an upperdielectric ring surrounding the upper electrode 179, an upper electrodeextension surrounding the upper dielectric ring, a lower dielectric ringsurrounding a lower electrode of the ESC 177, a lower electrodeextension surrounding the lower dielectric ring, an upper plasmaexclusion zone (PEZ) ring, a lower PEZ ring, etc. The upper electrode179 is located opposite to and facing the ESC 177. A work piece 131,e.g., a semiconductor wafer, etc., is supported on an upper surface 183of the ESC 177. Various processes, e.g., chemical vapor deposition,cleaning, deposition, sputtering, etching, ion implantation, resiststripping, etc., are performed on the work piece 131 during production.Integrated circuits, e.g., application specific integrated circuit(ASIC), programmable logic device (PLD), etc. are developed on the workpiece 131 and the integrated circuits are used in a variety ofelectronic items, e.g., cell phones, tablets, smart phones, computers,laptops, networking equipment, etc. Each of the lower electrode and theupper electrode 179 is made of a metal, e.g., aluminum, alloy ofaluminum, copper, etc.

In one embodiment, the upper electrode 179 includes a hole that iscoupled to a central gas feed (not shown). The central gas feed receivesone or more process gases from a gas supply (not shown). Examples of aprocess gases include an oxygen-containing gas, such as O₂. Otherexamples of a process gas include a fluorine-containing gas, e.g.,tetrafluoromethane (CF₄), sulfur hexafluoride (SF₆), hexafluoroethane(C₂F₆), etc. The upper electrode 179 is grounded. The ESC 177 is coupledto the x MHz RF generator and the y MHz RF generator via the impedancematching circuit 114.

When the process gas is supplied between the upper electrode 179 and theESC 177 and when the x MHz RF generator and/or the y MHz RF generatorsupplies RF signals via the impedance matching circuit 114 and the RFtransmission line 113 to the ESC 177, the process gas is ignited togenerate plasma within the plasma chamber 175.

When the x MHz RF generator generates and provides an RF signal via thenode N3, the impedance matching circuit 114, and the RF transmissionline 113 to the ESC 177 and when the y MHz generator generates andprovides an RF signal via the node N5, the impedance matching circuit114, and the RF transmission line 113 to the ESC 177, the VI probe 110measures the complex voltage and current at the node N3 and the VI probe111 measures the complex voltage and current at the node N5.

The complex voltages and currents measured by the VI probes 110 and 111are provided via corresponding communication devices 185 and 189 fromthe corresponding VI probes 110 and 111 to a storage hardware unit (HU)162 of a host system 130 for storage. For example, the complex voltageand current measured by the VI probe 110 is provided via thecommunication device 185 and a cable 191 to the host system 130 and thecomplex voltage and current measured by the VI probe 111 is provided viathe communication device 189 and a cable 193 to the host system 130.Examples of a communication device include an Ethernet device thatconverts data into Ethernet packets and converts Ethernet packets intodata, an Ethernet for Control Automation Technology (EtherCAT) device, aserial interface device that transfers data in series, a parallelinterface device that transfers data in parallel, a Universal Serial Bus(USB) interface device, etc.

Examples of the host system 130 include a computer, e.g., a desktop, alaptop, a tablet, etc. As an illustration, the host system 130 includesa processor and the storage HU 162. As used herein, a processor may be acentral processing unit (CPU), a microprocessor, an application specificintegrated circuit (ASIC), a programmable logic device (PLD), etc.Examples of the storage HU include a read-only memory (ROM), a randomaccess memory (RAM), or a combination thereof. The storage HU may be aflash memory, a redundant array of storage disks (RAID), a hard disk,etc.

The impedance matching model 104 is stored within the storage HU 162.The impedance matching model 104 has similar characteristics, e.g.,capacitances, inductances, complex power, complex voltage and currents,etc., as that of the impedance matching circuit 114. For example, theimpedance matching model 104 has the same number of capacitors and/orinductors as that within the impedance matching circuit 114, and thecapacitors and/or inductors are connected with each other in the samemanner, e.g., serial, parallel, etc. as that within the impedancematching circuit 114. To provide an illustration, when the impedancematching circuit 114 includes a capacitor coupled in series with aninductor, the impedance matching model 104 also includes the capacitorcoupled in series with the inductor.

As an example, the impedance matching circuit 114 includes one or moreelectrical components and the impedance matching model 104 includes adesign, e.g., a computer-generated model, of the impedance matchingcircuit 114. The computer-generated model may be generated by aprocessor based upon input signals received from a user via an inputhardware unit. The input signals include signals regarding whichelectrical components, e.g., capacitors, inductors, etc., to include ina model and a manner, e.g., series, parallel, etc., of coupling theelectrical components with each other. As another example, the impedancecircuit 114 includes hardware electrical components and hardwareconnections between the electrical components and the impedance matchingmodel 104 include software representations of the hardware electricalcomponents and of the hardware connections. As yet another example, theimpedance matching model 104 is designed using a software program andthe impedance matching circuit 114 is made on a printed circuit board.As used herein, electrical components may include resistors, capacitors,inductors, connections between the resistors, connections between theinductors, connections between the capacitors, and/or connectionsbetween a combination of the resistors, inductors, and capacitors.

Similarly, a cable model 163 and the cable 150 have similarcharacteristics, and a cable model 165 and the cable 152 has similarcharacteristics. As an example, an inductance of the cable model 163 isthe same as an inductance of the cable 150. As another example, thecable model 163 is a computer-generated model of the cable 150 and thecable model 165 is a computer-generated model of the cable 152.Similarly, an RF transmission model 161 and the RF transmission line 113have similar characteristics. For example, the RF transmission model 161has the same number of capacitors and/or inductors as that within the RFtransmission line 113, and the capacitors and/or inductors are connectedwith each other in the same manner, e.g., serial, parallel, etc. as thatwithin the RF transmission line 113. To further illustrate, when the RFtransmission line 113 includes a capacitor coupled in parallel with aninductor, the RF transmission model 161 also includes the capacitorcoupled in parallel with the inductor. As yet another example, the RFtransmission line 113 includes one or more electrical components and theRF transmission model 161 includes a design, e.g., a computer-generatedmodel, of the RF transmission line 113.

Based on the complex voltage and current received from the VI probe 110via the cable 191 and characteristics, e.g., capacitances, inductances,etc., of elements, e.g., inductors, capacitors, etc., within theimpedance matching model 104, the processor of the host system 130calculates a complex voltage and current V, I, and □, e.g., a secondcomplex voltage and current, at the output, e.g., the model node N4 m,of the impedance matching model 104. The complex voltage and current atthe model node N4 m is stored in the storage HU 162 and/or anotherstorage HU, e.g., a compact disc, a flash memory, etc., of the hostsystem 130. The complex V, I, and □ includes a voltage magnitude V, acurrent magnitude I, and a phase □ between the voltage and current.

The output of the impedance matching model 104 is coupled to an input ofthe RF transmission model 161, which is stored in the storage hardwareunit 162. The impedance matching model 104 also has an input, e.g., anode N3 m, which is used to receive the complex voltage and currentmeasured at the node N3.

The RF transmission model 161 includes the portion 173, another portion197, and an output N2 m. An input of the portion 173 is the input of theRF transmission model 161. An output of the portion 173 is coupled to aninput of the portion 197. The portion 173 has similar characteristics asthat of the portion 169 and the portion 197 has similar characteristicsas that of the portion 195.

Based on the complex voltage and current measured at the model node N4m, the processor of the host system 130 calculates a complex voltage andcurrent V, I, and □, e.g., a third complex voltage and current, at theoutput, e.g., the model node N1 m, of the portion 173 of the RFtransmission model 161. The complex voltage and current determined atthe model node N1 m is stored in the storage HU 162 and/or anotherstorage HU, e.g., a compact disc, a flash memory, etc., of the hostsystem 130.

In several embodiments, instead of or in addition to determining thethird complex voltage and current, the processor of the host system 130computes a complex voltage and current, e.g., an intermediate complexvoltage and current V, I, and □, at a point, e.g., a node, etc., withinthe portion 173 based on the complex voltage and current at the outputof the impedance matching model 104 and characteristics of elementsbetween the input of the RF transmission model 161 and the point withinthe portion 173.

In various embodiments, instead of or in addition to determining thethird complex voltage and current, the processor of the host system 130computes a complex voltage and current, e.g., an intermediate complexvoltage and current V, I, and □, at a point, e.g., a node, etc., withinthe portion 197 based on the complex voltage and current at the outputof the impedance matching model 104 and characteristics of elementsbetween the input of the RF transmission model 161 and the point withinthe portion 197.

It should further be noted that in some embodiments, the complex voltageand current at the output of the impedance matching model 104 iscalculated based on the complex voltage and current at the output of thex MHz RF generator, characteristics of elements the cable model 163, andcharacteristics of the impedance matching model 104.

It should be noted that although two generators are shown coupled to theimpedance matching circuit 114, in one embodiment, any number of RFgenerators, e.g., a single generator, three generators, etc., arecoupled to the plasma chamber 175 via an impedance matching circuit. Forexample, a 2 MHz generator, a 27 MHz generator, and a 60 MHz generatormay be coupled to the plasma chamber 175 via an impedance matchingcircuit. For example, although the above-described embodiments aredescribed with respect to using complex voltage and current measured atthe node N3, in various embodiments, the above-described embodiments mayalso use the complex voltage and current measured at the node N5.

FIG. 2 is a flowchart of an embodiment of a method 102 for determiningthe complex voltage and current at the output of the RF transmissionmodel portion 173 (FIG. 1). The method 102 is executed by one or moreprocessors of the host system 130 (FIG. 1). In an operation 106, thecomplex voltage and current, e.g., the first complex voltage andcurrent, measured at the node N3 is identified from within the storageHU 162 (FIG. 1). For example, it is determined that the first complexvoltage and current is received from the voltage probe 110 (FIG. 1). Asanother example, based on an identity, of the voltage probe 110, storedwithin the storage HU 162 (FIG. 1), it is determined that the firstcomplex voltage and current is associated with the identity.

Furthermore, in an operation 107, the impedance matching model 104(FIG. 1) is generated based on electrical components of the impedancematching circuit 114 (FIG. 1). For example, connections betweenelectrical components of the impedance matching circuit 114 andcharacteristics of the electrical components are provided to theprocessor of the host system 130 by the user via an input device that iscoupled with the host system 130. Upon receiving the connections and thecharacteristics, the processor generates elements that have the samecharacteristics as that of electrical components of the impedancematching circuit 114 and generates connections between the elements thathave the same connections as that between the electrical components.

The input, e.g., the node N3 m, of the impedance matching model 104receives the first complex voltage and current. For example, theprocessor of the host system 130 accesses, e.g., reads, etc., from thestorage HU 162 the first complex voltage and current and provides thefirst complex voltage and current to the input of the impedance matchingmodel 104 to process the first complex voltage and current.

In an operation 116, the first complex voltage and current is propagatedthrough one or more elements of the impedance matching model 104(FIG. 1) from the input, e.g., the node N3 m (FIG. 1), of the impedancematching model 104 to the output, e.g., the node N4 m (FIG. 1), of theimpedance matching model 104 to determine the second complex voltage andcurrent, which is at the output of the impedance matching model 104. Forexample, with reference to FIG. 3B, when the 2 MHz RF generator is on,e.g., operational, powered on, etc., a complex voltage and current Vx1,Ix1, and □x1, e.g., an intermediate complex voltage and current, whichincludes the voltage magnitude Vx1, the current magnitude Ix1, and thephase □x1 between the complex voltage and current, at a node 251, e.g.,an intermediate node, is determined based on a capacitance of acapacitor 253, based on a capacitance of a capacitor C5, and based onthe first complex voltage and current that is received at an input 255.Moreover, a complex voltage and current Vx2, Ix2, and □x2 at a node 257is determined based on the complex voltage and current Vx1, Ix1, and□x1, and based on an inductance of an inductor L3. The complex voltageand current Vx2, Ix2, and □x2 includes the voltage magnitude Vx2, thecurrent magnitude Ix2, and the phase □x2 between the voltage andcurrent. When the 27 MHz RF generator and the 60 MHz RF generator areoff, e.g., nonoperational, powered off, etc., a complex voltage andcurrent V2, I2, and □2 is determined to be the second complex voltageand current at an output 259, which is an example of the output, e.g.,the model node N4 m (FIG. 1), of the impedance matching model 104 (FIG.1). The complex voltage and current V2, I2, and □2 is determined basedon the complex voltage and current Vx2, Ix2, and □x2 and an inductor ofan inductor L2. The complex voltage and current V2, I2, and □2 includesthe voltage magnitude V2, the current magnitude I2, and the phase □2between the voltage and current.

Similarly, when 27 MHz RF generator is on and the 2 MHz and the 60 MHzRF generators are off, a complex voltage and current V27, I27, and □27at the output 259 is determined based on a complex voltage and currentreceived at a node 261 and characteristics of an inductor LPF2, acapacitor C3, a capacitor C4, and an inductor L2. The complex voltageand current V27, I27, and □27 includes the voltage magnitude V27, thecurrent magnitude I27, and the phase □27 between the voltage andcurrent. The complex voltage and current received at the node 261 is thesame as the complex voltage and current measured at the node N5 (FIG.1). When both the 2 MHz and 27 MHz RF generators are on and the 60 MHzRF generator is off, the complex voltages and currents V2, I2, □2, V27,I27, and □27 are an example of the second complex voltage and current.Moreover, similarly, when the 60 MHz RF generator is on and the 2 and 27MHz RF generators are off, a complex voltage and current V60, I60, and□60 at the output 259 is determined based on a complex voltage andcurrent received at a node 265 and characteristics of an inductor LPF1,a capacitor C1, a capacitor C2, an inductor L4, a capacitor 269, and aninductor L1. The complex voltage and current V60, I60, and □60 includesthe voltage magnitude V60, the current magnitude I60, and the phase □60between the voltage and current. When the 2 MHz, 27 MHz, and the 60 MHzRF generators are on, the complex voltages and currents V2, I2, □2, V27,I27, □27, V60, I60, and □60 are an example of the second complex voltageand current.

In an operation 117, the RF transmission model 161 (FIG. 1) is generatedbased on the electrical components of the RF transmission line 113 (FIG.1). For example, connections between electrical components of the RFtransmission line 113 and characteristics of the electrical componentsare provided to the processor of the host system 130 by the user via aninput device that is coupled with the host system 130. Upon receivingthe connections and the characteristics, the processor generateselements that have the same characteristics as that of electricalcomponents of the RF transmission line 113 and generates connectionsbetween the elements that are the same as that between the electricalcomponents.

In an operation 119, the second complex voltage and current ispropagated through one or more elements of the RF transmission modelportion 173 from the input of the RF transmission model portion 173 tothe output, e.g., the model node N1 m (FIG. 1), of the RF transmissionmodel portion 173 to determine the third complex voltage and current atthe output of the RF transmission model portion 173. For example, withreference to FIG. 5B, when the 2 MHz RF generator is on and the 27 and60 MHz RF generators are off, a complex voltage and current Vx4, Ix4,and □x4, e.g., an intermediate complex voltage and current, at a node293, e.g., an intermediate node, is determined based on an inductance ofan inductor Ltunnel, based on a capacitance of a capacitor Ctunnel, andbased on the complex voltage and current V2, I2, and □2 (FIG. 3B), whichis an example of the second complex voltage and current. It should benoted that Ltunnel is an inductance of a computer-generated model of anRF tunnel and Ctunnel is a capacitance of the RF tunnel model. Moreover,a complex voltage and current V21, I21, and □21 at an output 297 of atunnel and strap model 210 is determined based on the complex voltageand current Vx4, Ix4, and □x4, and based on an inductance of an inductorLstrap. The output 297 is an example of the output, e.g., the model nodeN1 m (FIG. 1), of the portion 173 (FIG. 1). It should be noted thatLstrap is an inductance of a computer-generated model of the RF strap.When the 2 MHz RF generator is on and the 27 and 60 MHz RF generatorsare off, e.g., nonoperational, powered off, etc., the complex voltageand current V21, I21, and □21 is determined to be the third complexvoltage and current at the output 297.

Similarly, when the 27 MHz RF generator is on and the 2 and 60 MHz RFgenerators are off, a complex voltage and current V271, I271, and □271at the output 297 is determined based on the complex voltage and currentV27, I27, □27 (FIG. 3B) at the output 259 and characteristics of theinductor Ltunnel, the capacitor Ctunnel, and the inductor Lstrap. Whenboth the 2 MHz and 27 MHz RF generators are on and the 60 MHz RFgenerator is off, the complex voltages and currents V21, I21, □21, V271,I271, and □271 are an example of the third complex voltage and current.

Moreover, similarly, when the 60 MHz RF generator is powered on and the2 and 27 MHz RF generators are powered off, a complex voltage andcurrent V601, I601, and □601 at the output 297 is determined based onthe complex voltage and current V60, I60, and □60 (FIG. 3B) received ata node 259 and characteristics of the inductor Ltunnel, the capacitorCtunnel, and the inductor Lstrap. When the 2 MHz, 27 MHz, and the 60 MHzRF generators are on, the complex voltages and currents V21, I21, □21,V271, I271, □271, V601, I601, and □601 are an example of the thirdcomplex voltage and current. The method 102 ends after the operation119.

FIG. 3A is a block diagram of an embodiment of a system 123 used toillustrate an impedance matching circuit 122. The impedance matchingcircuit 122 is an example of the impedance matching circuit 114 (FIG.1). The impedance matching circuit 122 includes series connectionsbetween electrical components and/or parallel connections betweenelectrical components.

FIG. 3B is a circuit diagram of an embodiment of an impedance matchingmodel 172. The impedance matching model 172 is an example of theimpedance matching model 104 (FIG. 1). As shown, the impedance matchingmodel 172 includes capacitors having capacitances C1 thru C9, inductorshaving inductances LPF1, LPF2, and L1 thru L4. It should be noted thatthe manner in which the inductors and/or capacitors are coupled witheach other in FIG. 3B is an example. For example, the inductors and/orcapacitors shown in FIG. 3B can be coupled in a series and/or parallelmanner with each other. Also, in some embodiments, the impedancematching model 172 includes a different number of capacitors and/or adifferent number of inductors than that shown in FIG. 3B.

FIG. 4 is a diagram of an embodiment of a system 178 used to illustratean RF transmission line 181, which is an example of the RF transmissionline 113 (FIG. 1). The RF transmission line 181 includes a cylinder 148,e.g., a tunnel. Within a hollow of the cylinder 148 lies an insulator190 and an RF rod 142. A combination of the cylinder 148 and the RF rod142 is an example of the portion 169 (FIG. 1) of the RF transmissionline 113 (FIG. 1). The RF transmission line 113 is bolted via bolts B1,B2, B3, and B4 with the impedance matching circuit 114. In oneembodiment, the RF transmission line 113 is bolted via any number ofbolts with the impedance matching circuit 114. In some embodiments,instead of or in addition to bolts, any other form of attachment, e.g.,glue, screws, etc., is used to attach the RF transmission line 113 tothe impedance matching circuit 114.

The RF transmission rod 142 is coupled with the output of the impedancematching circuit 114. Also, an RF strap 144, also known as RF spoon, iscoupled with the RF rod 142 and an RF rod 199, a portion of which islocated within a support 146, e.g., a cylinder. In an embodiment, acombination of the cylinder 148, the RF rod 142, the RF strap 144, thecylinder 146 and the RF rod 199 forms an RF transmission line 181, whichis an example of the RF transmission line 113 (FIG. 1). The support 146provides support to the plasma chamber. The support 146 is attached tothe ESC 177 of the plasma chamber. An RF signal is supplied from the xMHz generator via the cable 150, the impedance matching circuit 114, theRF rod 142, the RF strap 144, and the RF rod 199 to the ESC 177.

In one embodiment, the ESC 177 includes a heating element and anelectrode on top of the heating element. In an embodiment, the ESC 177includes a heating element and the lower electrode. In one embodiment,the ESC 177 includes the lower electrode and a heating element, e.g.,coil wire, etc., embedded within holes formed within the lowerelectrode. In some embodiments, the electrode is made of a metal, e.g.,aluminum, copper, etc. It should be noted that the RF transmission line181 supplies an RF signal to the lower electrode of the ESC 177.

FIG. 5A is a block diagram of an embodiment of a system 171 used toillustrate a circuit model 176 of the RF transmission line 113 (FIG. 1).For example, the circuit model 176 includes inductors and/or capacitors,connections between the inductors, connections between the capacitors,and/or connections between the inductors and the capacitors. Examples ofconnections include series and/or parallel connections. The circuitmodel 176 is an example of the RF transmission model 161 (FIG. 1).

FIG. 5B is a diagram of an embodiment of an electrical circuit 180 usedto illustrate a tunnel and strap model 210, which is an example of theportion 173 (FIG. 1) of the RF transmission model 161 (FIG. 1). Theelectrical circuit 180 includes the impedance matching model 172 and thetunnel and strap model 210. The tunnel and strap model 210 includesinductors Ltunnel and Lstrap and a capacitor Ctunnel. It should be notedthat the inductor Ltunnel represents an inductance of the cylinder 148(FIG. 4) and the RF rod 142 and the capacitor Ctunnel represents acapacitance of the cylinder 148 and the RF rod 142. Moreover, theinductor Lstrap represents an inductance of the RF strap 144 (FIG. 4).

In an embodiment, the tunnel and strap model 210 includes any number ofinductors and/or any number of capacitors. In this embodiment, thetunnel and strap model 210 includes any manner, e.g., serial, parallel,etc. of coupling a capacitor to another capacitor, coupling a capacitorto an inductor, and/or coupling an inductor to another inductor.

FIG. 6 is a block diagram of an embodiment of a system 200 for using avariable determined by the method 102 (FIG. 2). The system 200 includesa plasma chamber 135, which further includes an ESC 201 and has an input285. The plasma chamber 135 is an example of the plasma chamber 175(FIG. 1) and the ESC 201 is an example of the ESC 177 (FIG. 1). The ESC201 includes a heating element 198. Also, the ESC 201 is surrounded byan edge ring (ER) 194. The ER 194 includes a heating element 196. In anembodiment, the ER 194 facilitates a uniform etch rate and reduced etchrate drift near an edge of the work piece 131 that is supported by theESC 201.

A power supply 206 provides power to the heating element 196 via afilter 208 to heat the heating element 196 and a power supply 204provides power to the heating element 198 via a filter 202 to heat theheating element 198. In an embodiment, a single power supply providespower to both the heating elements 196 and 198. The filter 208 filtersout predetermined frequencies of a power signal that is received fromthe power supply 206 and the filter 202 filters out predeterminedfrequencies of a power signal that is received from the power supply204.

The heating element 198 is heated by the power signal received from thepower supply 204 to maintain an electrode of the ESC 201 at a desirabletemperature to further maintain an environment within the plasma chamber135 at a desirable temperature. Moreover, the heating element 196 isheated by the power signal received from the power supply 206 tomaintain the ER 194 at a desirable temperature to further maintain anenvironment within the plasma chamber 135 at a desirable temperature.

It should be noted that in an embodiment, the ER 194 and the ESC 201include any number of heating elements and any type of heating elements.For example, the ESC 201 includes an inductive heating element or ametal plate. In one embodiment, each of the ESC 201 and the ER 194includes one or more cooling element, e.g., one or more tubes that allowpassage of cold water, etc., to maintain the plasma chamber 135 at adesirable temperature.

It should further be noted that in one embodiment, the system 200includes any number of filters. For example, the power supplies 204 and206 are coupled to the ESC 201 and the ER 194 via a single filter.

FIG. 7A is a diagram of an embodiment of a system 217 used to illustratea model of the filters 202 and 208 (FIG. 6) to improve an accuracy ofthe variable. The system 217 includes the tunnel and strap model 210that is coupled to a model 216, which includes capacitors and/orinductors, and connections therebetween of the filters 202 and 208. Themodel 216 is stored within the storage HU 162 (FIG. 1) and/or the otherstorage HU. The capacitors and/or inductors of the model 216 are coupledwith each other in a manner, e.g., a parallel manner, a serial manner, acombination thereof, etc. The model 216 represents capacitances and/orinductances of the filters 202 and 208.

Moreover, the system 217 includes a cylinder model 211, which is acomputer-generated model of the RF rod 199 (FIG. 4) and the support 146(FIG. 4). The cylinder model 211 has similar characteristics as that ofelectrical components of the RF rod 199 and the support 146. Thecylinder model 211 includes one or more capacitors, one or moreinductors, connections between the inductors, connections between thecapacitors, and/or connections between a combination of the capacitorsand inductors.

The processor of the host system 130 (FIG. 1) calculates a combinedimpedance, e.g., total impedance, etc., of the model 216, the tunnel andstrap model 210, and the cylinder model 211. The combined impedanceprovides a complex voltage and impedance at the node N2 m. With theinclusion of the model 216 and the tunnel and strap model 210 indetermining the variable at the node N2 m, accuracy of the variable isimproved. It should be noted that an output of the model 216 is themodel node N2 m.

FIG. 7B is a diagram of an embodiment of a system 219 used to illustratea model of the filters 202 and 208 (FIG. 6) to improve an accuracy ofthe variable. The system 219 includes the tunnel and strap model 210 anda model 218, which is coupled in parallel to the tunnel and strap model210. The model 218 is an example of the model 216 (FIG. 7A). The model218 includes an inductor Lfilter, which represents a combined inductanceof the filters 202 and 208. The model 218 further includes a capacitorCfilter, which represents directed combined capacitance of the filters202 and 208.

FIG. 8 is a block diagram of an embodiment of a system 236 for using aVI probe 238 to measure the variable at an output 231 of an RF generator220. The output 231 is an example of the node N3 (FIG. 1) or of the nodeN5 (FIG. 1). The RF generator 220 is an example of the x MHz generatoror the y MHz generator (FIG. 1). The host system 130 generates andprovides a digital pulsing signal 213 having two or more states to adigital signal processor (DSP) 226. In one embodiment, the digitalpulsing signal 213 is a transistor-transistor logic (TTL) signal.Examples of the states include an on state and an off state, a statehaving a digital value of 1 and a state having a digital value of 0, ahigh state and a low state, etc.

In another embodiment, instead of the host system 130, a clockoscillator, e.g., a crystal oscillator, is used to generate an analogclock signal, which is converted by an analog-to-digital converter intoa digital signal similar to the digital pulsing signal 213.

The digital pulsing signal 213 is sent to the DSP 226. The DSP 226receives the digital pulsing signal 213 and identifies the states of thedigital pulsing signal 213. For example, the DSP 226 determines that thedigital pulsing signal 213 has a first magnitude, e.g., the value of 1,the high state magnitude, etc., during a first set of time periods andhas a second magnitude, e.g., the value of 0, the low state magnitude,etc., during a second set of time periods. The DSP 226 determines thatthe digital pulsing signal 213 has a state S1 during the first set oftime periods and has a state S0 during the second set of time periods.Examples of the state S0 include the low state, the state having thevalue of 0, and the off state. Examples of the state S1 include the highstate, the state having the value of 1, and the on state. As yet anotherexample, the DSP 226 compares a magnitude of the digital pulsing signal213 with a pre-stored value to determine that the magnitude of thedigital pulsing signal 213 is greater than the pre-stored value duringthe first set of time periods and that the magnitude during the state S0of the digital pulsing signal 213 is not greater than the pre-storedvalue during the second set of time periods. In the embodiment in whichthe clock oscillator is used, the DSP 226 receives an analog clocksignal from the clock oscillator, converts the analog signal into adigital form, and then identifies the two states S0 and S1.

When a state is identified as S1, the DSP 226 provides a power value P1and/or a frequency value F1 to a parameter control 222. Moreover, whenthe state is identified as S0, the DSP 226 provides a power value P0and/or a frequency value F0 to a parameter control 224. An example of aparameter control that is used to tune a frequency includes an autofrequency tuner (AFT).

It should be noted that the parameter control 222, the parameter control224, and the DSP 226 are portions of a control system 187. For example,the parameter control 222 and the parameter control 224 are logicblocks, e.g., tuning loops, which are portions of a computer programthat is executed by the DSP 226. In some embodiments, the computerprogram is embodied within a non-transitory computer-readable medium,e.g., a storage HU.

In an embodiment, a controller, e.g., hardware controller, ASIC, PLD,etc., is used instead of a parameter control. For example, a hardwarecontroller is used instead of the parameter control 222 and anotherhardware controller is used instead of the parameter control 224.

Upon receiving the power value P1 and/or the frequency value F1, theparameter control 222 provides the power value P1 and/or the frequencyvalue F1 to a driver 228 of a drive and amplifier system (DAS) 232.Examples of a driver includes a power driver, a current driver, avoltage driver, a transistor, etc. The driver 228 generates an RF signalhaving the power value P1 and/or the frequency value F1 and provides theRF signal to an amplifier 230 of the DAS 232.

In one embodiment, the driver 228 generates an RF signal having a drivepower value that is a function of the power value P1 and/or having adrive frequency value that is a function of the frequency value F1. Forexample, the drive power value is within a few, e.g. 1 thru 5, watts ofthe power value P1 and the drive frequency value is within a few, e.g. 1thru 5, Hz of the frequency value F1.

The amplifier 230 amplifies the RF signal having the power value P1and/or the frequency value F1 and generates an RF signal 215 thatcorresponds to the RF signal received from the driver 228. For example,the RF signal 215 has a higher amount of power than that of the powervalue P1. As another example, the RF signal 215 has the same amount ofpower as that of the power value P1. The RF signal 215 is transferredvia a cable 223 and the impedance matching circuit 114 to the knownload.

The cable 223 is an example of the cable 150 or the cable 152 (FIG. 1).For example, when the RF generator 220 is an example of the x MHz RFgenerator (FIG. 1), the cable 223 is an example of the cable 150 andwhen the RF generator 220 is an example of the y MHz RF generator (FIG.1), the cable 223 is an example of the cable 152.

When the power value P1 and/or the frequency value F1 are provided tothe DAS 232 by the parameter control 222 and the RF signal 215 isgenerated, a VI probe 238 measures values of the variable at the output231 that is coupled to the cable 223. The VI probe 238 is an example ofthe VI probe 110 or the VI probe 111 (FIG. 1). The VI probe 238 sendsthe values of the variable via a communication device 233 to the hostsystem 130 for the host system 130 to execute the method 102 (FIG. 2)and other methods described herein. The communication device 233 is anexample of the communication device 185 or 189 (FIG. 1). Thecommunication device 233 applies a protocol, e.g., Ethernet, EtherCAT,USB, serial, parallel, packetization, depacketization, etc., to transferdata from the VI probe 238 to the host system 130. In variousembodiments, the host system 130 includes a communication device thatapplies the protocol applied by the communication device 233. Forexample, when the communication 233 applies packetization, thecommunication device of the host system 130 applies depacketization. Asanother example, when the communication 233 applies a serial transferprotocol, the communication device of the host system 130 applies aserial transfer protocol.

Similarly, upon receiving the power value P0 and/or the frequency valueF0, the parameter control 224 provides the power value P0 and/or thefrequency value F0 to the driver 228. The driver 228 creates an RFsignal having the power value P0 and/or the frequency value F0 andprovides the RF signal to the amplifier 230.

In one embodiment, the driver 228 generates an RF signal having a drivepower value that is a function of the power value P0 and/or having adrive frequency value that is a function of the frequency value F0. Forexample, the drive power value is within a few, e.g. 1 thru 5, watts ofthe power value P0 and the drive frequency value is within a few, e.g. 1thru 5, Hz of the frequency value F0.

The amplifier 230 amplifies the RF signal having the power value P0and/or the frequency value F0 and generates an RF signal 221 thatcorresponds to the RF signal received from the driver 228. For example,the RF signal 221 has a higher amount of power than that of the powervalue P0. As another example, the RF signal 221 has the same amount ofpower as that of the power value P0. The RF signal 221 is transferredvia the cable 223 and the impedance matching circuit 114 to the knownload.

When the power value P0 and/or the frequency value F0 are provided tothe DAS 232 by the parameter control 224 and the RF signal 221 isgenerated, the VI probe 238 measures values of the variable at theoutput 231. The VI probe 238 sends the values of the variable to thehost system 130 for the host system 130 to execute the method 102 (FIG.2).

It should be noted that the in one embodiment, the VI probe 238 isdecoupled from the DSP 226. It should further be noted that the RFsignal 215 generated during the state S1 and the RF signal 221 generatedduring the state S0 are portions of a combined RF signal. For example,the RF signal 215 is a portion of the combined RF signal that has ahigher amount of power than the RF signal 221, which is another portionof the combined RF signal.

FIG. 9 is a block diagram of an embodiment of a system 250 in which theVI probe 238 and the communication device 233 are located outside the RFgenerator 220. In FIG. 1, the VI probe 110 is located within the x MHzRF generator to measure the variable at the output of the x MHz RFgenerator. The VI probe 238 is located outside the RF generator 220 tomeasure the variable at the output 231 of the RF generator 220. The VIprobe 238 is associated, e.g., coupled, to the output 231 of the RFgenerator 220.

FIG. 10 is a block diagram of an embodiment of a system 128 in which thevalues of the variable determined using the system 126 of FIG. 1 areused. The system 128 includes an m MHz RF generator, an n MHz RFgenerator, an impedance matching circuit 115, an RF transmission line287, and a plasma chamber 134. The plasma chamber 134 may be similar tothe plasma chamber 175.

It should be noted that in an embodiment, the x MHz RF generator of FIG.1 is similar to the m MHz RF generator and the y MHz RF generator ofFIG. 1 is similar to the n MHz RF generator. As an example, x MHz isequal to m MHz and y MHz is equal to n MHz. As another example, the xMHz generator and the m MHz generators have similar frequencies and they MHz generator and the n MHz generator have similar frequencies. Anexample of similar frequencies is when the x MHz is within a window,e.g., within kHz or Hz, of the m MHz frequency. In some embodiments, thex MHz RF generator of FIG. 1 is not similar to the m MHz RF generatorand the y MHz RF generator of FIG. 1 is not similar to the n MHz RFgenerator.

It is further noted that in various embodiments, a different type ofsensor is used in each of the m MHz and n MHz RF generators than thatused in each of the x MHz and y MHz RF generators. For example, a sensorthat does not comply with the NIST standard is used in the m MHz RFgenerator. As another example, a voltage sensor that measures onlyvoltage is used in the m MHz RF generator.

It should further be noted that in an embodiment, the impedance matchingcircuit 115 is similar to the impedance matching circuit 114 (FIG. 1).For example, an impedance of the impedance matching circuit 114 is thesame as an impedance of the impedance matching circuit 115. As anotherexample, an impedance of the impedance matching circuit 115 is within awindow, e.g., within 10-20%, of the impedance of the impedance matchingcircuit 114. In some embodiments, the impedance matching circuit 115 isnot similar to the impedance matching circuit 114.

The impedance matching circuit 115 includes electrical components, e.g.,inductors, capacitors, etc. to match an impedance of a power sourcecoupled to the impedance matching circuit 115 with an impedance of aload coupled to the circuit 115. For example, the impedance matchingcircuit 114 matches an impedance of the m MHz and n MHz RF generatorswith an impedance of the plasma chamber 134. In one embodiment,impedance matching circuit 115 is tuned to facilitate a match between animpedance of m MHz and n MHz RF generators coupled to the impedancematching circuit 115 and an impedance of a load.

It should be noted that in an embodiment, the RF transmission line 287is similar to the RF transmission line 113 (FIG. 1). For example, animpedance of the RF transmission line 287 is the same as an impedance ofthe RF transmission line 113. As another example, an impedance of the RFtransmission line 287 is within a window, e.g., within 10-20%, of theimpedance of the RF transmission line 113. In various embodiments, theRF transmission line 287 is not similar to the RF transmission line 113.

The plasma chamber 134 includes an ESC 192, an upper electrode 264, andother parts (not shown), e.g., an upper dielectric ring surrounding theupper electrode 264, an upper electrode extension surrounding the upperdielectric ring, a lower dielectric ring surrounding a lower electrodeof the ESC 192, a lower electrode extension surrounding the lowerdielectric ring, an upper plasma exclusion zone (PEZ) ring, a lower PEZring, etc. The upper electrode 264 is located opposite to and facing theESC 192. A work piece 262, e.g., a semiconductor wafer, etc., issupported on an upper surface 263 of the ESC 192. Each of the upperelectrode 264 and the lower electrode of the ESC 192 is made of a metal,e.g., aluminum, alloy of aluminum, copper, etc.

In one embodiment, the upper electrode 264 includes a hole that iscoupled to a central gas feed (not shown). The central gas feed receivesone or more process gases from a gas supply (not shown). Examples of aprocess gases include an oxygen-containing gas, such as O₂. Otherexamples of a process gas include a fluorine-containing gas, e.g.,tetrafluoromethane (CF₄), sulfur hexafluoride (SF₆), hexafluoroethane(C₂F₆), etc. The upper electrode 264 is grounded. The ESC 192 is coupledto the m MHz RF generator and the n MHz RF generator via the impedancematching circuit 115.

When the process gas is supplied between the upper electrode 264 and theESC 192 and when the m MHz RF generator or the n MHz RF generatorsupplies power via the impedance matching circuit 115 to the ESC 192,the process gas is ignited to generate plasma within the plasma chamber134.

It should be noted that the system 128 lacks a probe, e.g., a metrologytool, a VI probe, a voltage probe, etc., to measure the variable at anoutput 283 of the impedance matching circuit 115 or at a point on the RFtransmission line 287. The values of the variable at the model nodes N1m, N2 m, and N4 m are used to determine whether the system 128 isfunctioning as desired.

It should also be noted that in an embodiment, the system 128 includesany number of RF generators coupled to an impedance matching circuit.

FIGS. 11A, 11B, and 11C are diagrams of embodiments of graphs 268, 272,and 275 that illustrate a correlation between voltage, e.g., root meansquare (RMS) voltage, etc., that is measured at the output, e.g., thenode N4, of the impedance matching circuit 114 (FIG. 1) within thesystem 126 (FIG. 1) by using a voltage probe and a voltage, e.g., peakvoltage, etc., at a corresponding model node output, e.g., the node N4m, determined using the method 102 (FIG. 2). Moreover, FIGS. 11A thru11C are diagrams of embodiments of graphs 270, 274, and 277 thatillustrate a correlation between current, e.g., RMS current, etc., thatis measured the output, e.g., the node N4, of the system 126 (FIG. 1) byusing a current probe and a current, e.g., RMS current, etc., at acorresponding output, e.g., the node N4 m, determined using the method102 (FIG. 2).

The voltage determined using the method 102 is plotted on an x-axis ineach graph 268, 272, and 275 and the voltage determined using thevoltage probe is plotted on a y-axis in each graph 268, 272, and 275.Similarly, the current determined using the method 102 is plotted on anx-axis in each graph 270, 274, and 277 and the current determined usingthe current probe is plotted on a y-axis in each graph 270, 274, and277.

The voltages are plotted in the graph 268 when the x MHz RF generator isoperational, e.g., powered on, etc., and the y MHz RF generator and a zMHz RF generator, e.g., 60 MHz RF generator, are nonoperational, e.g.,powered off, decoupled from the impedance matching circuit 114, etc.Moreover, the voltages are plotted in the graph 272 when the y MHz RFgenerator is operational and the x and z MHz RF generators arenonoperational. Also, the voltages are plotted in the graph 275 when thez MHz RF generator is operational and the x and y MHz RF generators arenonoperational.

Similarly, currents are plotted in the graph 270 when the x MHz RFgenerator is operational, e.g., powered on, etc., and the y MHz RFgenerator and a z MHz RF generator are nonoperational, e.g., poweredoff, etc. Also, the currents are plotted in the graph 274 when the y MHzRF generator is operational and the x and z MHz RF generators arenonoperational. Also, the currents are plotted in the graph 277 when thez MHz RF generator is operational and the x and y MHz RF generators arenonoperational.

It can be seen in each graph 268, 272, and 275 that an approximatelylinear correlation exists between the voltage plotted on the y-axis ofthe graph and the voltage plotted on the x-axis of the graph. Similarly,it can be seen in each graph 270, 274, and 277 that an approximatelylinear correlation exists between the current plotted on the y-axis andthe current plotted on the x-axis.

FIG. 12A is a diagram of an embodiment of graphs 276 and 278 toillustrate that there is a correlation between a wired wafer biasmeasured using a sensor tool, e.g., a metrology tool, a probe, a sensor,etc., a model bias that is determined using the method 102 (FIG. 2) anda mathematical conversion, e.g., an equation, a formula, etc., and anerror in the model bias The wired wafer bias that is plotted in thegraph 276 is measured at a point, e.g., a node, on the RF transmissionline 113, e.g., the node N1, the node N2, etc., of the system 126(FIG. 1) and the model bias that is plotted in the graph 276 isdetermined at the corresponding model point, e.g., the model node N1 m,the model node N2 m, etc. (FIG. 1), on the RF transmission model 161(FIG. 1). The wired wafer bias is plotted along a y-axis in the graph276 and the model bias is plotted along an x-axis in the graph 276.

The wired wafer bias and the model bias are plotted in the graph 276when the x MHz RF generator is operational, and the y and z MHz RFgenerators are nonoperational. Moreover, the model bias of graph 276 isdetermined using an equation a2*V2+b2*I2+c2*sqrt(P2)+d2, where “*”represents multiplication, sqrt represents a square root, “V2”represents voltage at an output of the impedance matching model 104, I2represents current at the output of the impedance matching model 104, P2represents power at the output of the impedance matching model 104, “a2”is a coefficient, “b2” is a coefficient, “c2” is a coefficient, and “d2”is a constant value.

The graph 278 plots an error, which is an error at a model node on theRF transmission line model 161 (FIG. 1), e.g., at the node N1 m, at thenode N2 m, etc. (FIG. 1), on a y-axis and plots the model bias at themodel point on an x-axis. The model error is an error, e.g., a variance,a standard deviation, etc., in the model bias. The model error and themodel bias are plotted in the graph 278 when the x MHz RF generator isoperational and the y and z MHz RF generators are nonoperational.

FIG. 12B is a diagram of an embodiment of graphs 280 and 282 toillustrate that there is a correlation between a wired wafer bias, amodel bias that is determined using the method 102 (FIG. 2) and amathematical conversion, and an error in the model bias. The graphs 280and 282 are plotted in a manner similar to the graphs 276 and 278 (FIG.12A) except that the graphs 280 and 282 are plotted when the y MHz RFgenerator is operational and the x and z MHz RF generators arenonoperational. Moreover, the model bias of the graphs 280 and 282 isdetermined using an equation a27*V27+b27*I27+c27*sqrt (P27)+d27, where“V27” represents voltage at an output of the impedance matching model104, I27 represents current at the output of the impedance matchingmodel 104, P27 represents power at the output of the impedance matchingmodel 104, “a27” is a coefficient, “b27” is a coefficient, “c27” is acoefficient, and “d27” is a constant value.

FIG. 12C is a diagram of an embodiment of graphs 284 and 286 toillustrate that there is a correlation between a wired wafer bias, amodel bias that is determined using the method 102 (FIG. 2) and amathematical conversion, and an error in the model bias. The graphs 284and 286 are plotted in a manner similar to the graphs 276 and 278 (FIG.12A) except that the graphs 284 and 286 are plotted when the z MHz RFgenerator is operational and the x and y MHz RF generators arenonoperational. Moreover, the model bias of the graphs 284 and 286 isdetermined using an equation a60*V60+b60*160+c60*sqrt (P60)+d60, where“V60” represents voltage at an output of the impedance matching model104, I60 represents current at the output of the impedance matchingmodel 104, P60 represents power at the output of the impedance matchingmodel 104, “a60” is a coefficient, “b60” is a coefficient, “c60” is acoefficient, and “d60” is a constant value.

FIG. 12D is a diagram of an embodiment of graphs 288 and 290 toillustrate that there is a correlation between a wired wafer bias, amodel bias that is determined using the method 102 (FIG. 2) and amathematical conversion, and an error in the model bias. The graphs 288and 290 are plotted in a manner similar to the graphs 276 and 278 (FIG.12A) except that the graphs 288 and 290 are plotted when the x and y MHzRF generators are operational, and the z MHz RF generator isnonoperational. Moreover, the model bias of the graphs 288 and 290 isdetermined using an equation a2*V2+b2*I2+c2*sqrt(P2)+d27*V27+e27*I27+f27*sqrt (P27)+g227, where “d27”, “e27” and “f27”are coefficients, and “g227” is a constant value.

FIG. 12E is a diagram of an embodiment of graphs 292 and 294 toillustrate that there is a correlation between a wired wafer bias, amodel bias that is determined using the method 102 (FIG. 2) and amathematical conversion, and an error in the model bias. The graphs 292and 294 are plotted in a manner similar to the graphs 276 and 278 (FIG.12A) except that the graphs 292 and 294 are plotted when the x and z MHzRF generators are operational, and the y MHz RF generator isnonoperational. Moreover, the model bias of the graphs 292 and 294 isdetermined using an equation a2*V2+b2*I2+c2*sqrt(P2)+d60*V60+e60*160+f60*sqrt (P60)+g260, where “d60”, “e60” and “f60”are coefficients, and “g260” is a constant value.

FIG. 12F is a diagram of an embodiment of graphs 296 and 298 toillustrate that there is a correlation between a wired wafer bias, amodel bias that is determined using the method 102 (FIG. 2) and amathematical conversion, and an error in the model bias. The graphs 296and 298 are plotted in a manner similar to the graphs 276 and 278 (FIG.12A) except that the graphs 296 and 298 are plotted when the y and z MHzRF generators are operational, and the x MHz RF generator isnonoperational. Moreover, the model bias of the graphs 296 and 298 isdetermined using an equation a27*V27+b27*I27+c27*sqrt(P27)+d60*V60+e60*160+f60*sqrt (P60)+g2760, where “a27”, “b27” and “c27”are coefficients, and “g2760” is a constant value.

FIG. 12G is a diagram of an embodiment of graphs 302 and 304 toillustrate that there is a correlation between a wired wafer bias, amodel bias that is determined using the method 102 (FIG. 2) and amathematical conversion, and an error in the model bias. The graphs 302and 304 are plotted in a manner similar to the graphs 276 and 278 (FIG.12A) except that the graphs 302 and 304 are plotted when the x, y and zMHz RF generators are operational. Moreover, the model bias of thegraphs 302 and 304 is determined using an equation a2*V2+b2*I2+c2*sqrt(P2)+d60*V60+e60*160+f60*sqrt (P60)+g27*V27+h27*I27+i27*sqrt(P27)+j22760, where “g27”, “h27”, and “i27” are coefficients and“j22760” is a constant value.

FIG. 13 is a block diagram of an embodiment of the host system 130. Thehost system 130 includes a processor 168, the storage HU 162, an inputHU 320, an output HU 322, an input/output (I/O) interface 324, an I/Ointerface 326, a network interface controller (NIC) 328, and a bus 330.The processor 168, the storage HU 162, the input HU 320, the output HU322, the I/O interface 324, the I/O interface 326, and the NIC 328 arecoupled with each other via the bus 330. Examples of the input HU 320include a mouse, a keyboard, a stylus, etc. Examples of the output HU322 include a display, a speaker, or a combination thereof. The displaymay be a liquid crystal display, a light emitting diode display, acathode ray tube, a plasma display, etc. Examples of the NIC 328 includea network interface card, a network adapter, etc.

Examples of an I/O interface include an interface that providescompatibility between pieces of hardware coupled to the interface. Forexample, the I/O interface 324 converts a signal received from the inputHU 320 into a form, amplitude, and/or speed compatible with the bus 330.As another example, the I/O interface 326 converts a signal receivedfrom the bus 330 into a form, amplitude, and/or speed compatible withthe output HU 322.

It is noted that although the above-described embodiments are describedwith reference to parallel plate plasma chamber, in one embodiment, theabove-described embodiments apply to other types of plasma chambers,e.g., a plasma chamber including an inductively coupled plasma (ICP)reactor, a plasma chamber including an electron-cyclotron resonance(ECR) reactor, etc. For example, the x MHz RF generator and the y MHz RFgenerator are coupled to an inductor within the ICP plasma chamber.

It should be noted that although the above-described embodiments relateto providing an RF signal to the electrode of the ESC 177 (FIG. 1) andthe ESC 192 (FIG. 10), and grounding the upper electrodes 179 and 264(FIGS. 1 and 10), in several embodiments, the RF signal is provided tothe upper electrodes 179 and 264 while the lower electrodes of the ESCs177 and 163 are grounded.

Embodiments described herein may be practiced with various computersystem configurations including hand-held hardware units, microprocessorsystems, microprocessor-based or programmable consumer electronics,minicomputers, mainframe computers and the like. The embodiments canalso be practiced in distributed computing environments where tasks areperformed by remote processing hardware units that are linked through anetwork.

With the above embodiments in mind, it should be understood that theembodiments can employ various computer-implemented operations involvingdata stored in computer systems. These operations are those requiringphysical manipulation of physical quantities. Any of the operationsdescribed herein that form part of the embodiments are useful machineoperations. The embodiments also relates to a hardware unit or anapparatus for performing these operations. The apparatus may bespecially constructed for a special purpose computer. When defined as aspecial purpose computer, the computer can also perform otherprocessing, program execution or routines that are not part of thespecial purpose, while still being capable of operating for the specialpurpose. In some embodiments, the operations may be processed by ageneral purpose computer selectively activated or configured by one ormore computer programs stored in the computer memory, cache, or obtainedover a network. When data is obtained over a network the data may beprocessed by other computers on the network, e.g., a cloud of computingresources.

One or more embodiments can also be fabricated as computer-readable codeon a non-transitory computer-readable medium. The non-transitorycomputer-readable medium is any data storage hardware unit that canstore data, which can be thereafter be read by a computer system.Examples of the non-transitory computer-readable medium include harddrives, network attached storage (NAS), ROM, RAM, compact disc-ROMs(CD-ROMs), CD-recordables (CD-Rs), CD-rewritables (CD-RWs), magnetictapes and other optical and non-optical data storage hardware units. Thenon-transitory computer-readable medium can include computer-readabletangible medium distributed over a network-coupled computer system sothat the computer-readable code is stored and executed in a distributedfashion.

Although the method operations in the flowchart of FIG. 2 above weredescribed in a specific order, it should be understood that otherhousekeeping operations may be performed in between operations, oroperations may be adjusted so that they occur at slightly differenttimes, or may be distributed in a system which allows the occurrence ofthe processing operations at various intervals associated with theprocessing, as long as the processing of the overlay operations areperformed in the desired way.

One or more features from any embodiment may be combined with one ormore features of any other embodiment without departing from the scopedescribed in various embodiments described in the present disclosure.

Although the foregoing embodiments have been described in some detailfor purposes of clarity of understanding, it will be apparent thatcertain changes and modifications can be practiced within the scope ofthe appended claims. Accordingly, the present embodiments are to beconsidered as illustrative and not restrictive, and the embodiments arenot to be limited to the details given herein, but may be modifiedwithin the scope and equivalents of the appended claims.

1. A method for determining a value of a variable on a radio frequency(RF) transmission model, the method comprising: receiving a firstcomplex voltage and current measured at an output of an RF generatorwhen the RF generator is coupled to a plasma chamber via an impedancematching circuit, the impedance matching circuit having an input coupledto the output of the RF generator and an output coupled to an RFtransmission line; generating an impedance matching model based onelectrical components defined in the impedance matching circuit, theimpedance matching model having an input and an output, the impedancematching model having one or more elements; propagating the firstcomplex voltage and current through the one or more elements from theinput of the impedance matching model to the output of the impedancematching model to determine a second complex voltage and current,wherein the second complex voltage and current is at the output of theimpedance matching model; generating an RF transmission model based oncircuit components defined in the RF transmission line, the RFtransmission model having an input and an output, the input of the RFtransmission model coupled to the output of the impedance matchingmodel, the RF transmission model having a portion that includes one ormore elements; and propagating the second complex voltage and currentthrough the one or more elements of the RF transmission model portionfrom the input of the RF transmission model to an output of the RFtransmission model portion to determine a third complex voltage andcurrent, wherein the third complex voltage and current is at the outputof the RF transmission model portion.
 2. The method of claim 1, whereinthe first complex voltage and current received is measured at the outputof the RF generator with a voltage and current probe, the voltage andcurrent probe calibrated according to a pre-set formula.
 3. The methodof claim 2, wherein the pre-set formula is a standard.
 4. The method ofclaim 3, wherein the standard is a National Institute of Standards andTechnology (NIST) standard, wherein the voltage and current probe iscoupled with an open circuit, a short circuit, or a load to calibratethe voltage and current probe to comply with the NIST standard.
 5. Themethod of claim 1, wherein the third complex voltage and currentincludes a voltage value, a current value, and a phase between thevoltage value and the current value.
 6. The method of claim 1, whereinthe output of the RF generator is used to transfer an RF signal to theplasma chamber via the impedance matching circuit and the RFtransmission line.
 7. The method of claim 1, wherein the electricalcomponents of the impedance matching circuit include capacitors,inductors, or a combination thereof.
 8. The method of claim 1, whereinthe elements of the impedance matching model include capacitors,inductors, or a combination thereof.
 9. The method of claim 1, whereinthe electrical components of impedance matching circuit include acombination of capacitors and inductors, wherein the elements of theimpedance matching model have similar characteristics as that of theelectrical components of the impedance matching circuit.
 10. The methodof claim 1, wherein the third complex voltage and current at the outputof the RF transmission model portion is for use in a system, wherein thesystem includes an impedance matching circuit and excludes a metrologytool at an output of the impedance matching circuit of the system,wherein the system includes an RF transmission line and excludes ametrology tool at a point on the RF transmission line of the system. 11.The method of claim 1, wherein the impedance matching model and the RFtransmission model are generated within a computer.
 12. The method ofclaim 1, wherein propagating the first complex voltage and currentthrough the one or more elements from the input of the impedancematching model to the output of the impedance matching model todetermine the second complex voltage and current comprises: determiningan intermediate complex voltage and current within an intermediate nodewithin the impedance matching model based on the first complex voltageand current and characteristics of one or more elements of the impedancematching model coupled between the input of the impedance matching modeland the intermediate node; and determining the second complex voltageand current based on the intermediate complex voltage and current andcharacteristics of one or more elements of the impedance matching modelcoupled between the intermediate node and the output of the impedancematching model.
 13. The method of claim 1, wherein the circuitcomponents of the RF transmission line include a combination ofcapacitors and inductors, wherein the elements of the RF transmissionmodel have similar characteristics as that of the circuit components ofthe RF transmission line.
 14. The method of claim 1, wherein propagatingthe second complex voltage and current through the one or more elementsof the RF transmission model portion from the input of the RFtransmission model to the output of the RF transmission model portion todetermine the third complex voltage and current comprises: determiningan intermediate complex voltage and current within an intermediate nodewithin the RF transmission model portion based on the second complexvoltage and current and characteristics of one or more elements of theRF transmission model portion coupled between the input of the RFtransmission model and the intermediate node; and determining the thirdcomplex voltage and current based on the intermediate complex voltageand current and characteristics of the one or more elements of the RFtransmission model portion coupled between the intermediate node and theoutput of the RF transmission model portion.
 15. A plasma system fordetermining a value of a variable on a radio frequency (RF) transmissionmodel, comprising: an RF generator for generating an RF signal; animpedance matching circuit coupled to the RF generator; a plasma chambercoupled to the impedance matching circuit via an RF transmission line,the impedance matching circuit having an input coupled to an output ofthe RF generator and an output coupled to the RF transmission line; anda processor coupled to the RF generator, the processor for: receiving afirst complex voltage and current measured at the output of the RFgenerator; generating an impedance matching model based on electricalcomponents defined in the impedance matching circuit, the impedancematching model having an input and an output, the impedance matchingmodel having one or more elements; propagating the first complex voltageand current through the one or more elements from the input of theimpedance matching model to the output of the impedance matching modelto determine a second complex voltage and current, wherein the secondcomplex voltage and current is at the output of the impedance matchingmodel; generating an RF transmission model based on electricalcomponents defined in the RF transmission line, the RF transmissionmodel having an input and an output, the input of the RF transmissionmodel coupled to the output of the impedance matching model, the RFtransmission model having a portion that includes one or more elements;propagating the second complex voltage and current through the one ormore elements of the RF transmission model portion from the input of theRF transmission model to an output of the RF transmission model portionto determine a third complex voltage and current, wherein the thirdcomplex voltage and current is at the output of the RF transmissionmodel portion; and providing the third complex voltage and current forstorage to a storage hardware unit.
 16. The system of claim 15, whereinthe RF generator is associated with a voltage and current probe, whereinthe voltage and current probe is configured to measure the first complexvoltage and current at the output of the RF generator, wherein thevoltage and current probe is calibrated to comply with a pre-setformula.
 17. The system of claim 16, wherein the pre-set formula is astandard, wherein the standard is a National Institute of Standards andTechnology (NIST) standard, wherein the voltage and current probe iscoupled with an open circuit, a short circuit, or a load to calibratethe voltage and current probe to comply with the NIST standard.
 18. Acomputer system for determining a value of a variable on a radiofrequency (RF) transmission model, the computer system comprising: aprocessor configured to: receive a first complex voltage and currentmeasured at an output of an RF generator when the RF generator iscoupled to a plasma chamber via an impedance matching circuit, theimpedance matching circuit having an input coupled to the output of theRF generator and an output coupled to an RF transmission line; generatean impedance matching model based on electrical components defined inthe impedance matching circuit, the impedance matching model having aninput and an output, the impedance matching model having one or moreelements; propagate the first complex voltage and current through theone or more elements from the input of the impedance matching model tothe output of the impedance matching model to determine a second complexvoltage and current, wherein the second complex voltage and current isat the output of the impedance matching model; generate an RFtransmission model based on electrical components defined in the RFtransmission line, the RF transmission model having an input and anoutput, the input of the RF transmission model coupled to the output ofthe impedance matching model, the RF transmission model having a portionthat includes one or more elements; and propagate the second complexvoltage and current through the one or more elements of the RFtransmission model portion from the input of the RF transmission modelto an output of the RF transmission model portion to determine a thirdcomplex voltage and current, wherein the third complex voltage andcurrent is at the output of the RF transmission model portion; and amemory device coupled to the processor, the memory device configured tostore the third complex voltage and current.
 19. The computer system ofclaim 18, wherein the first complex voltage and current received ismeasured at the output of the RF generator with a voltage and currentprobe, the voltage and current probe calibrated according to a pre-setformula.
 20. The computer system of claim 19, wherein the pre-setformula is a standard, wherein the standard is a National Institute ofStandards and Technology (NIST) standard, wherein the voltage andcurrent probe is coupled with an open circuit, a short circuit, or aload to calibrate the voltage and current probe to comply with the NISTstandard.